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arXiv · 1109.1674

A Linear-Optical Proof that the Permanent is #P-Hard

Scott Aaronson
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Abstract

One of the crown jewels of complexity theory is Valiant's 1979 theorem that computing the permanent of an n*n matrix is #P-hard. Here we show that, by using the model of linear-optical quantum computing---and in particular, a universality theorem due to Knill, Laflamme, and Milburn---one can give a different and arguably more intuitive proof of this theorem.

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Scott Aaronson. 2011-09-08. A Linear-Optical Proof that the Permanent is #P-Hard. https://doi.org/10.1098/rspa.2011.0232

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